For a range of applications, it is useful to deduce the shape that a flexible optical fiber occupies in space using only measurements of light traveling within the fiber; this shape generally includes both bending and twisting deflections. Traditional shape estimation failed to address torsion. Such a failure is permissible in a torsionally rigid optical fiber, wherein bend states of direction and curvature fully and accurately describe the three-dimensional geometry of the optical fiber. However, torsional deflection of the optical fiber can make for entirely different geometries as compared to the geometry of a torsionally rigid optical fiber.
As shown in FIG. 1, a prior art method and apparatus 10 use fiber Bragg gratings 20 (“FBGs”) in a multi-core optical fiber 30 having multiple cores and a helical bias of some peripheral cores. See, e.g., C. G. Askins, et al., Proc. Bragg Gratings, Photosensitivity and Poling in Glass Waveguides 2007, JWA39, Quebec Canada, incorporated herein by reference, and C. G. Askins et al., OFC/NFOEC 2008 Tech. Digest, OMT3, San Diego Calif. (“Askins OFC 2008”), incorporated herein by reference. In that approach, local uniaxial strains sensed by the variously placed and oriented FBGs are used to deduce both bending and twisting. The prior art apparatus 10 includes a polarization controller 40, a charge-coupled device (“CCD”) spectrometer 50, a processor 60, and a broadband light source 70. The polarization controller 40 is computer-driven, and is capable of outputting any state of polarization (“SOP”) from any input SOP. The spectrometer 50 permits high-speed determination of the center wavelength of light reflected from the multiple FBGs. The processor 60 adjusts the controller in response to the wavelength measured by the spectrometer 50.
In addition to the physical bases of that approach, polarization-dependent reflectivity (“PDR”) is another optical effect in optical fibers bearing Bragg gratings which may be exploited. With PDR, the spectrum of light reflected by a FBG is seen to shift in wavelength depending on the SOP of the light illuminating it. In particular, when light is linearly polarized and aligned with the “slow” PDR axis, the longest Bragg reflection wavelength is observed; light polarized normal to this direction produces the shortest Bragg reflection wavelength (“Bragg wavelength” is used as shorthand for the midpoint or centroid of a FBG reflection spectrum having finite width). FIG. 2 shows an experimental graph of PDR, where two distinct reflection spectra are seen from the same FBG illuminated with orthogonal polarizations. PDR results both from intrinsic fiber birefringence and from the grating inscription process; the orientation of the two birefringence components may not necessarily align. The rotational orientation of the net birefringence is fixed with respect to the fiber, and is nearly unperturbed by significant bending or twisting for gratings in cores at the centerline of the fiber. While large lateral stresses can disturb PDR orientation and magnitude, such stresses may be avoided in many applications of interest.
According to this prior art method, a fiber-squeezing polarization scrambler is used to vary the SOP of light illuminating the FBG. Alternatively, any of several designs of polarization controller using various means of optical phase modulation (e.g., electro-optic modulation and adjustable bulk optics), are also capable of this function. The initial purpose of the scrambler is to rapidly vary the SOP to remove polarization sensitivity. However, an alternative to polarization scrambling is systematic modulation of SOP in response to rapid measurements of Bragg wavelength to permit tracking of the maximum (or minimum) PDR wavelength. The signals are monitored by CCD spectrometer to obtain a real-time feedback signal to adjust the force on three fiber-squeezing actuators, constituting an electro-mechanical polarization controller. Representative shifts in measured wavelength (vertical axis) are plotted versus time (horizontal axis) in FIG. 3. The signal represents how the measured Bragg wavelength is seen to vary as a representative sampling of all possible states of polarization (SOP) sequentially illuminate the FBG by use of a rapidly adjustable polarization controller. For the example, the strain state of the FBG is not varied during the measurement interval. The graph shows the smoothly-evolving nature of the signal, and its suitability for an algorithm which automatically “tracks” the maximum or minimum Bragg wavelength by applying adjustments to the polarization controller. Dashed line “A” is the maximum measured Bragg wavelength for a constant strain state: this occurs when light is linearly polarized and aligned with the slow birefringent axis at the location of the fiber Bragg grating (FBG). Dashed line “B” is the minimum measured Bragg wavelength: this occurs when light is linearly polarized and aligned with the fast birefringent axis at the location of the fiber Bragg grating (FBG).
Polarization controllers are commonly available and apply birefringence to an optical path (which may constitute, or be connected to, an optical fiber) and monitor the resulting SOP with a polarization analyzer. By way of example, Applicant's polarization tracking algorithm is described as follows. The polarization control is modified in response to a spectral measurement and finds and tracks maxima or minima of Bragg wavelengths, thereby maintaining polarization alignment with the FBG. Light from a broadband source is guided by a single-moded optical fiber which is subjected to lateral compression by three or more actuators. Each actuator modulates a compressive force along a direction perpendicular to the fiber's axis, and substantially differing from each of the other actuators. Each actuator is capable of applying sufficient stress to produce birefringence exceeding a full wave of phase difference. This configuration is sufficient to convert any input SOP to any other. The measured Bragg wavelength of an FBG is recorded as all squeezers are rapidly modulated. When the largest observed Bragg wavelength is identified, the squeezer drive signals are noted. From this point forward, the squeezers are only “dithered” over a reduced range and the Bragg wavelength monitored to guide small, frequent offsets to the average setting of each squeezer. Occasionally, the end of the adjustment range of a squeezer is approached, and a large step adjustment corresponding to a one-wave phase shift is applied toward the center of the squeezer's operational range. In the example, fiber squeezers are used to produce adjustable birefringence. Alternatively, electro-optic modulators, bulk optical elements, or other suitable phase modulation devices may be used for the same purpose. Examples of suitable commercial products include Adaptif model A3000 and Thorlabs model IPM5300.
Although the FBG is not disturbed (i.e., no changes in temperature or strain), when the birefringence-inducing fiber squeezers are modulated, the indicated strain also modulates. The computer or processor rapidly executes the above-mentioned algorithm to adjust fiber squeezer drive signals to converge on the maximum (or minimum) PDR wavelength, which amounts to establishing linearly polarized light aligned with the “slow” (or fast) PDR axis of the FBG. As a new strain state occurs in the fiber due to incremental bending or twisting, the algorithm is applied to re-establish polarization alignment with the FBG.